Assep princing workshop 2

This Jupyter Notebook describes all the code required to the Asset pricing workshop 2

# Importing packages required
import pandas as pd
import numpy as np
import pyreadstat
import pyarrow.feather as feather
import datetime
from datetime import date
import math 
import scipy.stats
import statsmodels.regression.linear_model as lm
import statsmodels.tools.tools as ct
pd.options.display.float_format = '{:,.4f}'.format # Reduce decimal points to 4
pd.pandas.set_option('display.max_columns', None)

# Visualisation
import matplotlib.pyplot as plt
import seaborn as sns
import plotly.express as px
import plotly.graph_objects as go

# Reading the database with the ETF and KF Factors values
df = pd.read_excel('DATOS Taller 2 AP 2022.xlsx', sheet_name='ETF_DB',index_col=0)
# df = pd.read_excel('C:/Users/Miguel Angel/OneDrive - Universidad EAFIT/2022-1/Asset pricing/Workshop/Workshop 2/DATOS Taller 2 AP 2022.xlsx', sheet_name='ETF_DB',index_col=0)

# Data exploration - visualization
df_plot = df.reset_index()
df_plot2=pd.melt(df_plot, id_vars =['DATE'], value_vars =['VTV', 'VGT', 'VB', 'USMV', 'PNQI', 'MTUM', 'XBI', 'SPHQ', 'ESGU','SECT', 'VUG', 'LRGF', 'ERP', 'SMB', 'HML', 'RF', 'MOM'])
fig = px.line(df_plot2, x="DATE", y="value", color='variable', title='ETFs values')
fig.show()


df_plot3=pd.melt(df_plot, id_vars =['DATE'], value_vars =['ERP', 'SMB', 'HML', 'RF', 'MOM'])
fig2 = px.line(df_plot3, x="DATE", y="value", color='variable', title='Factors values', color_discrete_sequence=px.colors.qualitative.Dark2)
fig2.show()

# To drop objets used
del [df_plot, fig, fig2, df_plot2, df_plot3]

# Database structure
df.info()

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 121 entries, 2012-02-29 to 2022-02-28
Data columns (total 17 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   VTV     121 non-null    float64
 1   VGT     121 non-null    float64
 2   VB      121 non-null    float64
 3   USMV    121 non-null    float64
 4   PNQI    121 non-null    float64
 5   MTUM    107 non-null    float64
 6   XBI     121 non-null    float64
 7   SPHQ    121 non-null    float64
 8   ESGU    63 non-null     float64
 9   SECT    54 non-null     float64
 10  VUG     121 non-null    float64
 11  LRGF    83 non-null     float64
 12  ERP     121 non-null    float64
 13  SMB     121 non-null    float64
 14  HML     121 non-null    float64
 15  RF      121 non-null    float64
 16  MOM     121 non-null    float64
dtypes: float64(17)
memory usage: 17.0 KB

It is noticed that for some variables there few missing values such as: MTUM, ESGU, SECT, and LRGF.

# Database main stats
df.describe()

	VTV	VGT	VB	USMV	PNQI	MTUM	XBI	SPHQ	ESGU	SECT	VUG	LRGF	ERP	SMB	HML	RF	MOM
count	121.0000	121.0000	121.0000	121.0000	121.0000	107.0000	121.0000	121.0000	63.0000	54.0000	121.0000	83.0000	121.0000	121.0000	121.0000	121.0000	121.0000
mean	94.2680	173.7803	135.7637	49.2444	112.0500	101.6284	74.4656	28.4374	70.4888	31.7255	143.0460	31.5708	0.0119	-0.0008	-0.0007	0.0004	0.0020
std	22.9167	105.7000	39.2722	14.0322	60.6486	38.0144	30.7528	9.6530	16.9232	5.8871	66.0860	6.1456	0.0398	0.0265	0.0326	0.0007	0.0356
min	53.7700	66.7500	72.6800	27.6380	37.7999	51.3700	25.6200	14.7400	49.1260	24.2900	66.3100	22.6100	-0.1338	-0.0832	-0.1402	0.0000	-0.1245
25%	79.2800	100.0000	111.2400	37.6800	68.2407	70.3999	51.3300	21.5800	58.3672	27.6383	99.6000	26.5850	-0.0019	-0.0189	-0.0183	0.0000	-0.0202
50%	93.4700	133.0000	130.9300	47.7200	92.3100	95.6800	74.0300	27.3300	64.5300	29.0763	120.4700	31.2500	0.0143	0.0016	-0.0038	0.0001	0.0036
75%	107.7600	213.5600	154.6100	60.6300	137.7653	120.8150	90.5400	33.2200	81.4200	35.3800	166.1800	33.7900	0.0319	0.0140	0.0130	0.0009	0.0216
max	147.1100	458.1700	229.4900	80.9000	256.6500	190.6800	152.8800	53.2100	107.9000	44.8700	320.9000	46.5600	0.1365	0.0706	0.1279	0.0021	0.1006

The ETF with higher standard deviation is the VGT.

# To calculate the monthly growth
returns = df.pct_change()

# Database returns main stats
returns.describe()

	VTV	VGT	VB	USMV	PNQI	MTUM	XBI	SPHQ	ESGU	SECT	VUG	LRGF	ERP	SMB	HML	RF	MOM
count	120.0000	120.0000	120.0000	120.0000	120.0000	106.0000	120.0000	120.0000	62.0000	53.0000	120.0000	82.0000	120.0000	120.0000	120.0000	72.0000	120.0000
mean	0.0086	0.0157	0.0096	0.0087	0.0139	0.0116	0.0142	0.0107	0.0123	0.0102	0.0126	0.0078	-2.8162	-5.3380	-0.4014	inf	-0.1945
std	0.0387	0.0477	0.0487	0.0323	0.0564	0.0413	0.0854	0.0357	0.0459	0.0477	0.0427	0.0438	20.0015	38.6725	19.7084	NaN	17.7556
min	-0.1558	-0.1008	-0.2224	-0.1185	-0.1169	-0.1193	-0.2799	-0.0990	-0.1296	-0.1272	-0.1083	-0.1555	-129.0000	-417.0000	-46.3333	-1.0000	-69.6667
25%	-0.0112	-0.0126	-0.0107	-0.0099	-0.0197	-0.0112	-0.0396	-0.0089	-0.0007	-0.0111	-0.0109	-0.0107	-1.8064	-2.0933	-1.9207	-0.0132	-2.0419
50%	0.0125	0.0204	0.0126	0.0115	0.0176	0.0144	0.0142	0.0129	0.0171	0.0180	0.0163	0.0113	-0.8480	-1.0913	-0.9273	0.0000	-1.0816
75%	0.0298	0.0448	0.0368	0.0312	0.0467	0.0368	0.0764	0.0336	0.0339	0.0375	0.0360	0.0313	0.1081	-0.0290	-0.1185	0.1295	0.0840
max	0.1276	0.1420	0.1578	0.0937	0.1667	0.1170	0.2060	0.1226	0.1329	0.1195	0.1508	0.1153	72.9091	14.7241	201.0000	inf	152.5000

The ETF with the higher simple return is VGT with 0.015731 (1.573%). And the ETF with the higher standard deviation is XBI with 0.0853.

# To create an index based on montlhy growth
df_index = returns.pct_change().fillna(0) \
  .add(1).cumprod().mul(100).reset_index()
df_indexfactor = df.add(1).cumprod().mul(100).reset_index()

# Data exploratory - visualization of indexes base 100

df_index_plot = df_index.reset_index()
df_index_plot=pd.melt(df_index_plot, id_vars =['DATE'], value_vars =['VTV', 'VGT', 'VB', 'USMV', 'PNQI', 'MTUM', 'XBI', 'SPHQ', 'ESGU','SECT', 'VUG', 'LRGF'])
fig3 = px.line(df_index_plot, x="DATE", y="value", color='variable', title='ETFs growth index (base 100)', color_discrete_sequence=px.colors.qualitative.Bold)
fig3.show()

df_indexfactor_plot = df_indexfactor.reset_index()
df_indexfactor_plot=pd.melt(df_indexfactor_plot, id_vars =['DATE'], value_vars =['ERP', 'SMB', 'HML', 'RF', 'MOM'])
fig4 = px.line(df_indexfactor_plot, x="DATE", y="value", color='variable', title='Factors growth index (base 100)', color_discrete_sequence=px.colors.qualitative.Dark2)
fig4.show()

# To drop objets used
del [df_index_plot, df_index, fig3, df_indexfactor, df_indexfactor_plot, fig4, returns]

# Calculating the log returns for every variable in the dataset
logreturns = np.log(df) - np.log(df.shift(1))
# lnreturns = np.log1p(df.pct_change())
# To replace the columns avoiding the returns calculation for factors
columns=['ERP', 'SMB', 'HML', 'RF', 'MOM']
logreturns[columns] = df[columns]
del [columns] # To drop the aux object
logreturns = logreturns.iloc[1: , :] # To drop the first row of the dataframe

# Database returns main stats
logreturns.describe()

	VTV	VGT	VB	USMV	PNQI	MTUM	XBI	SPHQ	ESGU	SECT	VUG	LRGF	ERP	SMB	HML	RF	MOM
count	120.0000	120.0000	120.0000	120.0000	120.0000	106.0000	120.0000	120.0000	62.0000	53.0000	120.0000	82.0000	120.0000	120.0000	120.0000	120.0000	120.0000
mean	0.0078	0.0145	0.0084	0.0082	0.0122	0.0107	0.0105	0.0100	0.0112	0.0091	0.0116	0.0068	0.0117	-0.0006	-0.0007	0.0005	0.0021
std	0.0390	0.0473	0.0495	0.0324	0.0559	0.0412	0.0864	0.0356	0.0460	0.0481	0.0425	0.0443	0.0399	0.0266	0.0327	0.0007	0.0358
min	-0.1694	-0.1062	-0.2515	-0.1261	-0.1244	-0.1270	-0.3284	-0.1043	-0.1388	-0.1360	-0.1146	-0.1690	-0.1338	-0.0832	-0.1402	0.0000	-0.1245
25%	-0.0112	-0.0127	-0.0107	-0.0100	-0.0199	-0.0113	-0.0404	-0.0089	-0.0007	-0.0112	-0.0110	-0.0108	-0.0036	-0.0191	-0.0184	0.0000	-0.0203
50%	0.0124	0.0202	0.0125	0.0114	0.0174	0.0143	0.0141	0.0128	0.0169	0.0178	0.0161	0.0112	0.0140	0.0021	-0.0039	0.0001	0.0038
75%	0.0294	0.0438	0.0361	0.0307	0.0456	0.0361	0.0736	0.0331	0.0333	0.0368	0.0353	0.0309	0.0315	0.0144	0.0135	0.0009	0.0218
max	0.1201	0.1328	0.1465	0.0896	0.1542	0.1107	0.1873	0.1157	0.1248	0.1129	0.1405	0.1091	0.1365	0.0706	0.1279	0.0021	0.1006

The ETF with the higher log return is VGT also with 0.014505 (1.4505%). And the ETF with the higher standard deviation is XBI also with 0.086356.

# Returns Data exploratory - visualization
df_plot = logreturns.reset_index()
df_plot2=pd.melt(df_plot, id_vars =['DATE'], value_vars =['VTV', 'VGT', 'VB', 'USMV', 'PNQI', 'MTUM', 'XBI', 'SPHQ', 'ESGU','SECT', 'VUG', 'LRGF', 'ERP', 'SMB', 'HML', 'RF', 'MOM'])
fig = px.line(df_plot2, x="DATE", y="value", color='variable', title='ETFs log return values', color_discrete_sequence=px.colors.qualitative.Safe)
fig.show()


df_plot3=pd.melt(df_plot, id_vars =['DATE'], value_vars =['ERP', 'SMB', 'HML', 'RF', 'MOM'])
fig2 = px.line(df_plot3, x="DATE", y="value", color='variable', title='Factors log values', color_discrete_sequence=px.colors.qualitative.Vivid)
fig2.show()

# To drop objets used
del [df_plot, fig, fig2, df_plot2, df_plot3]

# Data exploratory - visualization of return indexes base 100
df_indexfactor = logreturns.add(1).cumprod().mul(100).reset_index()
df_index_plot = df_indexfactor.reset_index()
df_index_plot=pd.melt(df_index_plot, id_vars =['DATE'], value_vars =['VTV', 'VGT', 'VB', 'USMV', 'PNQI', 'MTUM', 'XBI', 'SPHQ', 'ESGU','SECT', 'VUG', 'LRGF', 'ERP', 'SMB', 'HML', 'RF', 'MOM'])
fig3 = px.line(df_index_plot, x="DATE", y="value", color='variable', title='ETFs and Factors log return index (base 100)')
fig3.show()

# To drop objets used
del [df_index_plot, fig3, df_indexfactor]

1.1. To determine the statically significance of factors

# To calculate the mean by column
logreturns_mean=logreturns.mean(axis = 0, skipna = True)
# To calculate the std by column
logreturns_std=logreturns.std(axis = 0, skipna = True)
# To calculate the Z value by column
z_value = (logreturns_mean*math.sqrt(len(df.columns))/logreturns_std)

# It is created a dataframe to get all the information in one object
frame = {'z_value': z_value, 'mean': logreturns_mean, 'std': logreturns_std}
result = pd.DataFrame(frame)

# Find p-value
z_pvalue = pd.DataFrame(scipy.stats.norm.sf(abs(result.z_value))*2)
result.reset_index(inplace=True)
result['zpvalue'] = z_pvalue # To add the p value of the Z score for every factor (including the ETFs)
result

	index	z_value	mean	std	zpvalue
0	VTV	0.8247	0.0078	0.0390	0.4096
1	VGT	1.2651	0.0145	0.0473	0.2058
2	VB	0.6964	0.0084	0.0495	0.4862
3	USMV	1.0403	0.0082	0.0324	0.2982
4	PNQI	0.9012	0.0122	0.0559	0.3675
5	MTUM	1.0690	0.0107	0.0412	0.2851
6	XBI	0.4992	0.0105	0.0864	0.6177
7	SPHQ	1.1575	0.0100	0.0356	0.2471
8	ESGU	1.0017	0.0112	0.0460	0.3165
9	SECT	0.7771	0.0091	0.0481	0.4371
10	VUG	1.1276	0.0116	0.0425	0.2595
11	LRGF	0.6325	0.0068	0.0443	0.5271
12	ERP	1.2057	0.0117	0.0399	0.2279
13	SMB	-0.0957	-0.0006	0.0266	0.9237
14	HML	-0.0917	-0.0007	0.0327	0.9270
15	RF	2.8227	0.0005	0.0007	0.0048
16	MOM	0.2410	0.0021	0.0358	0.8095

According to the p value observed in the last table the factors ERP, SMB, HML and MOM showed to be statically different from zero. Which means that all the factors mentioned could give additional information about the ETF returns. Also, there is evidence that the returns provident by the ETF are statistically different from zero.

1.2. To calculate the returns in excess from each ETF.

# Calculating the return in excess for each ETF
logreturns['VTVn'] =logreturns['VTV'] -logreturns['RF']
logreturns['VGTn'] =logreturns['VGT'] -logreturns['RF']
logreturns['VBn'] =logreturns['VB'] -logreturns['RF']
logreturns['USMVn'] =logreturns['USMV'] -logreturns['RF']
logreturns['PNQIn'] =logreturns['PNQI'] -logreturns['RF']
logreturns['MTUMn'] =logreturns['MTUM'] -logreturns['RF']
logreturns['XBIn'] =logreturns['XBI'] -logreturns['RF']
logreturns['SPHQn'] =logreturns['SPHQ'] -logreturns['RF']
logreturns['ESGUn'] =logreturns['ESGU'] -logreturns['RF']
logreturns['SECTn'] =logreturns['SECT'] -logreturns['RF']
logreturns['VUGn'] =logreturns['VUG'] -logreturns['RF']
logreturns['LRGFn'] =logreturns['LRGF'] -logreturns['RF']

# Data exploratory - visualization of return indexes base 100
df_indexfactor = logreturns.add(1).cumprod().mul(100).reset_index()
df_index_plot = df_indexfactor.reset_index()
df_index_plot2=pd.melt(df_index_plot, id_vars =['DATE'], value_vars =['VTVn', 'VGTn', 'VBn', 'USMVn', 'PNQIn', 'MTUMn', 'XBIn', 'SPHQn', 'ESGUn', 'SECTn', 'VUGn', 'LRGFn'])
fig3 = px.line(df_index_plot2, x="DATE", y="value", color='variable', title='ETFs return in excess index (base 100)')
fig3.show()

df_index_plot3=pd.melt(df_index_plot, id_vars =['DATE'], value_vars =['VTV', 'VGT', 'VB', 'USMV', 'PNQI', 'MTUM', 'XBI', 'SPHQ', 'ESGU','SECT', 'VUG', 'LRGF'])
fig4 = px.line(df_index_plot3, x="DATE", y="value", color='variable', title='ETFs return index (base 100)')
fig4.show()

# To drop objets used
del [logreturns_mean, logreturns_std, z_pvalue, z_value, df_index_plot, fig3, df_indexfactor, fig4, df_index_plot2, df_index_plot3, frame]

1.3. Evaluating the ETF performance

# To calculate the mean by column
logreturns_mean=logreturns.mean(axis = 0, skipna = True)
# To calculate the std by column
logreturns_std=logreturns.std(axis = 0, skipna = True)
# It is created a dataframe to get all the information in one object
frame = {'ER': logreturns_mean, 'SIGMA': logreturns_std} # Expected returns (EP)
result = pd.DataFrame(frame)
result['SHARPE'] = result['ER'] / result['SIGMA']
result

	ER	SIGMA	SHARPE
VTV	0.0078	0.0390	0.2000
VGT	0.0145	0.0473	0.3068
VB	0.0084	0.0495	0.1689
USMV	0.0082	0.0324	0.2523
PNQI	0.0122	0.0559	0.2186
MTUM	0.0107	0.0412	0.2593
XBI	0.0105	0.0864	0.1211
SPHQ	0.0100	0.0356	0.2807
ESGU	0.0112	0.0460	0.2430
SECT	0.0091	0.0481	0.1885
VUG	0.0116	0.0425	0.2735
LRGF	0.0068	0.0443	0.1534
ERP	0.0117	0.0399	0.2924
SMB	-0.0006	0.0266	-0.0232
HML	-0.0007	0.0327	-0.0222
RF	0.0005	0.0007	0.6846
MOM	0.0021	0.0358	0.0585
VTVn	0.0073	0.0391	0.1879
VGTn	0.0141	0.0473	0.2971
VBn	0.0079	0.0496	0.1594
USMVn	0.0077	0.0325	0.2379
PNQIn	0.0118	0.0560	0.2103
MTUMn	0.0102	0.0413	0.2466
XBIn	0.0100	0.0864	0.1157
SPHQn	0.0095	0.0357	0.2673
ESGUn	0.0103	0.0461	0.2241
SECTn	0.0082	0.0483	0.1697
VUGn	0.0112	0.0425	0.2625
LRGFn	0.0061	0.0444	0.1382

# In the last table it is shown that the Expected RF in equal to 0.000453 (row 15 and column 1)
result['RF'] = result.iloc[15]['ER']
# result['RF'] = 0.0004533333333333336 

# To get all the Jessen's Alphas into a data frame it is created an empty dataframe
jalpha_df = pd.DataFrame()
# List of ETF
ETF_list = ['VTV', 'VGT', 'VB', 'USMV', 'PNQI', 'MTUM', 'XBI', 'SPHQ', 'ESGU', 'SECT', 'VUG', 'LRGF']

# list of models
models = []

for resp in ETF_list:
    formula = resp + " ~ ERP"
    models.append(lm.OLS.from_formula(formula, data = logreturns, hasconst=bool).fit())

# To extrac every parameter from models
jalpha_df['VTV']=models[0].params
jalpha_df['VGT']=models[1].params
jalpha_df['VB']=models[2].params
jalpha_df['USMV']=models[3].params
jalpha_df['PNQI']=models[4].params
jalpha_df['MTUM']=models[5].params
jalpha_df['XBI']=models[6].params
jalpha_df['SPHQ']=models[7].params
jalpha_df['ESGU']=models[8].params
jalpha_df['SECT']=models[9].params
jalpha_df['VUG']=models[10].params
jalpha_df['LRGF']=models[11].params

# print(models[11].summary())

# To get all the Jessen's Alphas pvalues into a data frame it is created an empty dataframe
pjalpha_df = pd.DataFrame()
# To extrac every parameter p value from models
pjalpha_df['VTV']=models[0].pvalues
pjalpha_df['VGT']=models[1].pvalues
pjalpha_df['VB']=models[2].pvalues
pjalpha_df['USMV']=models[3].pvalues
pjalpha_df['PNQI']=models[4].pvalues
pjalpha_df['MTUM']=models[5].pvalues
pjalpha_df['XBI']=models[6].pvalues
pjalpha_df['SPHQ']=models[7].pvalues
pjalpha_df['ESGU']=models[8].pvalues
pjalpha_df['SECT']=models[9].pvalues
pjalpha_df['VUG']=models[10].pvalues
pjalpha_df['LRGF']=models[11].pvalues

# To transpose the dataset
pjalpha_df = pjalpha_df.T
pjalpha_df.rename(columns = {'Intercept':'ALPHA_CAPM', 'ERP':'BETA_CAPM'}, inplace = True) # To rename the columns

# To get all the Jessen's Alphas R2 into a data frame it is created an empty dataframe
# To extrac every R2 from models
# Initializing list of lists
data = [['VTV',models[0].rsquared], ['VGT',models[1].rsquared], ['VB',models[2].rsquared], ['USMV',models[3].rsquared], ['PNQI',models[4].rsquared], ['MTUM',models[5].rsquared], ['XBI',models[6].rsquared], ['SPHQ',models[7].rsquared], ['ESGU',models[8].rsquared], ['SECT',models[9].rsquared], ['VUG',models[10].rsquared], ['LRGF',models[11].rsquared]]
# Creating the pandas DataFrame with the R2 for every model
models_r2 = pd.DataFrame(data, columns = ['index', 'CAPM'])
del [data]

# To get all the Jessen's Alphas R2 into a data frame it is created an empty dataframe
# To extrac every R2 from models
# Initializing list of lists
data = [['VTV',models[0].rsquared_adj], ['VGT',models[1].rsquared_adj], ['VB',models[2].rsquared_adj], ['USMV',models[3].rsquared_adj], ['PNQI',models[4].rsquared_adj], ['MTUM',models[5].rsquared_adj], ['XBI',models[6].rsquared_adj], ['SPHQ',models[7].rsquared_adj], ['ESGU',models[8].rsquared_adj], ['SECT',models[9].rsquared_adj], ['VUG',models[10].rsquared_adj], ['LRGF',models[11].rsquared_adj]]
# Creating the pandas DataFrame with the R2 for every model
models_r2a = pd.DataFrame(data, columns = ['index', 'CAPM'])
del [data]

# To clean the memory
del[formula, frame, models, resp, ETF_list, logreturns_std, logreturns_mean]

# To transpose the dataset
jalpha_df = jalpha_df.T
jalpha_df.rename(columns = {'Intercept':'ALPHA_CAPM', 'ERP':'BETA_CAPM'}, inplace = True) # To rename the columns

# Joining the result dataframe and the Jesen's Alpha dataframe to have a sinlge dataframe of results
result.reset_index(inplace=True)
jalpha_df.reset_index(inplace=True)
result = pd.merge(result, jalpha_df, how='left', left_on=['index'], right_on=['index'])
result = result.dropna(subset=['ALPHA_CAPM']) #Droping NA in the CAPM column
del [jalpha_df]

Treynor ratio

# Calculating the Treynor ratio
result['TR'] = (result['ER'] - result['RF']) / result['BETA_CAPM']

Fama and French 3 factors model

# To get all the Jessen's Alphas from the 3 factors FF model into a data frame it is created an empty dataframe
jalpha_df = pd.DataFrame()
# List of ETF
ETF_list = ['VTV', 'VGT', 'VB', 'USMV', 'PNQI', 'MTUM', 'XBI', 'SPHQ', 'ESGU', 'SECT', 'VUG', 'LRGF']

# list of models
models = []

for resp in ETF_list:
    formula = resp + " ~ ERP + SMB + HML"
    models.append(lm.OLS.from_formula(formula, data = logreturns, hasconst=bool).fit())

# To extrac every parameter from models
jalpha_df['VTV']=models[0].params
jalpha_df['VGT']=models[1].params
jalpha_df['VB']=models[2].params
jalpha_df['USMV']=models[3].params
jalpha_df['PNQI']=models[4].params
jalpha_df['MTUM']=models[5].params
jalpha_df['XBI']=models[6].params
jalpha_df['SPHQ']=models[7].params
jalpha_df['ESGU']=models[8].params
jalpha_df['SECT']=models[9].params
jalpha_df['VUG']=models[10].params
jalpha_df['LRGF']=models[11].params

# print(models[11].summary())

# To reshape DataFrame from wide format to long format
jalpha_df.reset_index(inplace=True)
jalpha_df.drop([1,2,3], axis=0, inplace=True)
jalpha_df = pd.melt(jalpha_df, id_vars='index', value_vars=['VTV', 'VGT', 'VB', 'USMV', 'PNQI', 'MTUM', 'XBI', 'SPHQ', 'ESGU', 'SECT', 'VUG', 'LRGF'])
del jalpha_df['index']
jalpha_df.rename(columns = {'value':'3FF', 'variable':'index'}, inplace = True) # To rename the columns
# Joining the result dataframe and the Jesen's Alpha dataframe to have a sinlge dataframe of results
result = pd.merge(result, jalpha_df, how='left', left_on=['index'], right_on=['index'])

# To get all the Jessen's Alphas pvalues into a data frame it is created an empty dataframe
pjalpha_df2 = pd.DataFrame()
# To extrac every parameter p value from models
pjalpha_df2['VTV']=models[0].pvalues
pjalpha_df2['VGT']=models[1].pvalues
pjalpha_df2['VB']=models[2].pvalues
pjalpha_df2['USMV']=models[3].pvalues
pjalpha_df2['PNQI']=models[4].pvalues
pjalpha_df2['MTUM']=models[5].pvalues
pjalpha_df2['XBI']=models[6].pvalues
pjalpha_df2['SPHQ']=models[7].pvalues
pjalpha_df2['ESGU']=models[8].pvalues
pjalpha_df2['SECT']=models[9].pvalues
pjalpha_df2['VUG']=models[10].pvalues
pjalpha_df2['LRGF']=models[11].pvalues

# To transpose the dataset
pjalpha_df2 = pjalpha_df2.T
pjalpha_df2.rename(columns = {'Intercept':'ALPHA_3FF', 'ERP':'BETA_3FF', 'SMB':'SMB_3FF', 'HML':'HML_3FF'}, inplace = True) # To rename the columns

pjalpha_df.reset_index(inplace=True)
pjalpha_df2.reset_index(inplace=True)
# Joining the result dataframe and the Jesen's Alpha dataframe to have a sinlge dataframe of results
pjalpha_df3 = pd.merge(pjalpha_df, pjalpha_df2, how='outer', left_on=['index'], right_on=['index'])

# To get all the Jessen's Alphas R2 into a data frame it is created an empty dataframe
# To extrac every R2 from models
# Initializing list of lists
data = [['VTV',models[0].rsquared], ['VGT',models[1].rsquared], ['VB',models[2].rsquared], ['USMV',models[3].rsquared], ['PNQI',models[4].rsquared], ['MTUM',models[5].rsquared], ['XBI',models[6].rsquared], ['SPHQ',models[7].rsquared], ['ESGU',models[8].rsquared], ['SECT',models[9].rsquared], ['VUG',models[10].rsquared], ['LRGF',models[11].rsquared]]
# Creating the pandas DataFrame with the R2 for every model
models3FF_r2 = pd.DataFrame(data, columns = ['index', '3FF'])
# Joining the result dataframe and the Jesen's Alpha dataframe to have a sinlge dataframe of results
models_r2 = pd.merge(models_r2, models3FF_r2, how='outer', left_on=['index'], right_on=['index'])

# To get all the Jessen's Alphas R2 into a data frame it is created an empty dataframe
# To extrac every R2 from models
# Initializing list of lists
data = [['VTV',models[0].rsquared_adj], ['VGT',models[1].rsquared_adj], ['VB',models[2].rsquared_adj], ['USMV',models[3].rsquared_adj], ['PNQI',models[4].rsquared_adj], ['MTUM',models[5].rsquared_adj], ['XBI',models[6].rsquared_adj], ['SPHQ',models[7].rsquared_adj], ['ESGU',models[8].rsquared_adj], ['SECT',models[9].rsquared_adj], ['VUG',models[10].rsquared_adj], ['LRGF',models[11].rsquared_adj]]
# Creating the pandas DataFrame with the R2 for every model
models3FF_r2a = pd.DataFrame(data, columns = ['index', '3FF'])
# Joining the result dataframe and the Jesen's Alpha dataframe to have a sinlge dataframe of results
models_r2a = pd.merge(models_r2a, models3FF_r2a, how='outer', left_on=['index'], right_on=['index'])

# To clean the memory
del[data, pjalpha_df, pjalpha_df2, models3FF_r2, jalpha_df, models, resp, ETF_list, formula]

Fama and French 3 factors model including momentum

# To get all the Jessen's Alphas from the 3 factors + MOM FF model into a data frame it is created an empty dataframe
jalpha_df = pd.DataFrame()
# List of ETF
ETF_list = ['VTV', 'VGT', 'VB', 'USMV', 'PNQI', 'MTUM', 'XBI', 'SPHQ', 'ESGU', 'SECT', 'VUG', 'LRGF']

# list of models
models = []

for resp in ETF_list:
    formula = resp + " ~ ERP + SMB + HML + MOM"
    models.append(lm.OLS.from_formula(formula, data = logreturns, hasconst=bool).fit())

# To extrac every parameter from models
jalpha_df['VTV']=models[0].params
jalpha_df['VGT']=models[1].params
jalpha_df['VB']=models[2].params
jalpha_df['USMV']=models[3].params
jalpha_df['PNQI']=models[4].params
jalpha_df['MTUM']=models[5].params
jalpha_df['XBI']=models[6].params
jalpha_df['SPHQ']=models[7].params
jalpha_df['ESGU']=models[8].params
jalpha_df['SECT']=models[9].params
jalpha_df['VUG']=models[10].params
jalpha_df['LRGF']=models[11].params

# print(models[11].summary())

# To reshape DataFrame from wide format to long format
jalpha_df.reset_index(inplace=True)
jalpha_df.drop([1,2,3,4], axis=0, inplace=True)
jalpha_df = pd.melt(jalpha_df, id_vars='index', value_vars=['VTV', 'VGT', 'VB', 'USMV', 'PNQI', 'MTUM', 'XBI', 'SPHQ', 'ESGU', 'SECT', 'VUG', 'LRGF'])
del jalpha_df['index']
jalpha_df.rename(columns = {'value':'3MFF', 'variable':'index'}, inplace = True) # To rename the columns
# Joining the result dataframe and the Jesen's Alpha dataframe to have a sinlge dataframe of results
result = pd.merge(result, jalpha_df, how='left', left_on=['index'], right_on=['index'])

# To get all the Jessen's Alphas pvalues into a data frame it is created an empty dataframe
pjalpha_df2 = pd.DataFrame()
# To extrac every parameter p value from models
pjalpha_df2['VTV']=models[0].pvalues
pjalpha_df2['VGT']=models[1].pvalues
pjalpha_df2['VB']=models[2].pvalues
pjalpha_df2['USMV']=models[3].pvalues
pjalpha_df2['PNQI']=models[4].pvalues
pjalpha_df2['MTUM']=models[5].pvalues
pjalpha_df2['XBI']=models[6].pvalues
pjalpha_df2['SPHQ']=models[7].pvalues
pjalpha_df2['ESGU']=models[8].pvalues
pjalpha_df2['SECT']=models[9].pvalues
pjalpha_df2['VUG']=models[10].pvalues
pjalpha_df2['LRGF']=models[11].pvalues

# To transpose the dataset
pjalpha_df2 = pjalpha_df2.T
pjalpha_df2.rename(columns = {'Intercept':'ALPHA_3MFF', 'ERP':'BETA_3MFF', 'SMB':'SMB_3MFF', 'HML':'HML_3MFF', 'MOM':'MOM_3MFF'}, inplace = True) # To rename the columns

pjalpha_df2.reset_index(inplace=True)
# Joining the result dataframe and the Jesen's Alpha dataframe to have a sinlge dataframe of results
pjalpha_df = pd.merge(pjalpha_df3, pjalpha_df2, how='outer', left_on=['index'], right_on=['index'])
del [pjalpha_df3, pjalpha_df2]

# To get all the Jessen's Alphas R2 into a data frame it is created an empty dataframe
# To extrac every R2 from models
# Initializing list of lists
data = [['VTV',models[0].rsquared], ['VGT',models[1].rsquared], ['VB',models[2].rsquared], ['USMV',models[3].rsquared], ['PNQI',models[4].rsquared], ['MTUM',models[5].rsquared], ['XBI',models[6].rsquared], ['SPHQ',models[7].rsquared], ['ESGU',models[8].rsquared], ['SECT',models[9].rsquared], ['VUG',models[10].rsquared], ['LRGF',models[11].rsquared]]
# Creating the pandas DataFrame with the R2 for every model
models3FF_r2 = pd.DataFrame(data, columns = ['index', '3MFF'])
# Joining the result dataframe and the Jesen's Alpha dataframe to have a sinlge dataframe of results
models_r2 = pd.merge(models_r2, models3FF_r2, how='outer', left_on=['index'], right_on=['index'])

# To get all the Jessen's Alphas R2 into a data frame it is created an empty dataframe
# To extrac every R2 from models
# Initializing list of lists
data = [['VTV',models[0].rsquared_adj], ['VGT',models[1].rsquared_adj], ['VB',models[2].rsquared_adj], ['USMV',models[3].rsquared_adj], ['PNQI',models[4].rsquared_adj], ['MTUM',models[5].rsquared_adj], ['XBI',models[6].rsquared_adj], ['SPHQ',models[7].rsquared_adj], ['ESGU',models[8].rsquared_adj], ['SECT',models[9].rsquared_adj], ['VUG',models[10].rsquared_adj], ['LRGF',models[11].rsquared_adj]]
# Creating the pandas DataFrame with the R2 for every model
models3FF_r2a = pd.DataFrame(data, columns = ['index', '3MFF'])
# Joining the result dataframe and the Jesen's Alpha dataframe to have a sinlge dataframe of results
models_r2a = pd.merge(models_r2a, models3FF_r2a, how='outer', left_on=['index'], right_on=['index'])

# To clean the memory
del[jalpha_df, models, resp, ETF_list, formula]

# Performance measures - visualization
fig = px.bar(result, x="index", y="SHARPE", title='Sharpe ratio for ETF')
fig.show()

fig3 = px.bar(result, x="index", y="TR", title='Treynor ratio for ETF', color_discrete_sequence=px.colors.qualitative.Pastel1)
fig3.show()

fig2 = px.bar(result, x="index", y="ALPHA_CAPM", title='Jensen Alpha for ETF', color_discrete_sequence=px.colors.qualitative.Set3)
fig2.show()

fig4 = px.bar(result, x="index", y="3FF", title='Fama and French 3 factors Alpha for ETF', color_discrete_sequence=px.colors.qualitative.Set1)
fig4.show()

fig5 = px.bar(result, x="index", y="3MFF", title='Fama and French 3 factors + momentum Alpha for ETF', color_discrete_sequence=px.colors.qualitative.Dark24)
fig5.show()

# To analize the pvalues for all the estimators from models
pjalpha_df

	index	ALPHA_CAPM	BETA_CAPM	ALPHA_3FF	BETA_3FF	SMB_3FF	HML_3FF	ALPHA_3MFF	BETA_3MFF	SMB_3MFF	HML_3MFF	MOM_3MFF
0	VTV	0.0244	0.0000	0.0002	0.0000	0.0000	0.0000	0.0004	0.0000	0.0000	0.0000	0.6715
1	VGT	0.2929	0.0000	0.4940	0.0000	0.0151	0.0000	0.4945	0.0000	0.0159	0.0000	0.9435
2	VB	0.0035	0.0000	0.0012	0.0000	0.0000	0.0171	0.0004	0.0000	0.0000	0.0019	0.0368
3	USMV	0.9733	0.0000	0.4936	0.0000	0.0000	0.5782	0.2777	0.0000	0.0000	0.5138	0.0206
4	PNQI	0.8414	0.0000	0.7743	0.0000	0.1154	0.0000	0.7860	0.0000	0.1212	0.0000	0.9543
5	MTUM	0.8402	0.0000	0.6650	0.0000	0.0674	0.0000	0.1414	0.0000	0.1593	0.0013	0.0000
6	XBI	0.4045	0.0000	0.7551	0.0000	0.0000	0.0000	0.5992	0.0000	0.0000	0.0000	0.2040
7	SPHQ	0.9862	0.0000	0.6276	0.0000	0.0005	0.9666	0.4836	0.0000	0.0009	0.5019	0.1961
8	ESGU	0.1718	0.0000	0.0176	0.0000	0.0000	0.0157	0.0162	0.0000	0.0000	0.0156	0.5144
9	SECT	0.1981	0.0000	0.3003	0.0000	0.4495	0.1070	0.1844	0.0000	0.1612	0.0061	0.0088
10	VUG	0.8711	0.0000	0.1676	0.0000	0.0000	0.0000	0.1467	0.0000	0.0000	0.0000	0.5717
11	LRGF	0.0032	0.0000	0.0036	0.0000	0.5829	0.0003	0.0021	0.0000	0.3880	0.0001	0.1531

# To analize the R2 from models
models_r2

	index	CAPM	3FF	3MFF
0	VTV	0.8825	0.9597	0.9598
1	VGT	0.8026	0.8649	0.8649
2	VB	0.8678	0.9611	0.9625
3	USMV	0.7538	0.8001	0.8092
4	PNQI	0.6207	0.7191	0.7191
5	MTUM	0.8131	0.8805	0.9247
6	XBI	0.3930	0.6704	0.6751
7	SPHQ	0.9246	0.9326	0.9336
8	ESGU	0.9867	0.9921	0.9922
9	SECT	0.9440	0.9486	0.9555
10	VUG	0.9054	0.9652	0.9653
11	LRGF	0.9420	0.9528	0.9540

# R2 measures - visualization
fig = px.bar(models_r2, x="index", y="CAPM", title='CAPM R2 for ETF', color_discrete_sequence=px.colors.qualitative.Antique)
fig.show()

fig2 = px.bar(models_r2, x="index", y="3FF", title='3 Factors model FF R2 for ETF', color_discrete_sequence=px.colors.qualitative.Pastel1)
fig2.show()

fig3 = px.bar(models_r2, x="index", y="3MFF", title='3 Factors model FF with Momentum R2 for ETF', color_discrete_sequence=px.colors.qualitative.Dark24)
fig3.show()

# R2 adjusted measures - visualization
fig = px.bar(models_r2a, x="index", y="CAPM", title='CAPM R2 adjusted for ETF', color_discrete_sequence=px.colors.qualitative.Vivid)
fig.show()

fig2 = px.bar(models_r2a, x="index", y="3FF", title='3 Factors model FF R2 adjusted for ETF', color_discrete_sequence=px.colors.qualitative.Pastel2)
fig2.show()

fig3 = px.bar(models_r2a, x="index", y="3MFF", title='3 Factors model FF with Momentum R2 adjusted for ETF', color_discrete_sequence=px.colors.qualitative.Set1)
fig3.show()

# Cleaning the memory
del [fig, fig2, fig3, fig4, fig5, models3FF_r2, df, data, models3FF_r2a]